Question

a man wants to adopt a puppy from an animal shelter. at the shelter, he finds eight puppies that he likes, a male and female puppy from each of the four breeds of beagle, bullmastiff, dachshund, and puli. the puppies are each so cute that he cannot make up his mind, so he decides to pick the dog randomly.
find the probability that the man chooses anything but a puli.
the probability is □. (type a simplified fraction.)

Explanation:

Step1: Calculate total number of puppies

There are \(4\) breeds and \(2\) puppies (male and female) per breed. So total number of puppies \(n(S)=4\times2 = 8\).

Step2: Calculate number of non - puli puppies

There are \(3\) non - puli breeds (beagle, bullmastiff, dachshund) and \(2\) puppies per non - puli breed. So number of non - puli puppies \(n(E)=3\times2=6\).

Step3: Use probability formula

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 6\) and \(n(S)=8\), we get \(P(E)=\frac{6}{8}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)